Algebra Examples

$2 w^{2} + 9 w - 10 = 6 w$

Step 1

Move all terms containing $w$ to the left side of the equation.

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Step 1.1

Subtract $6 w$ from both sides of the equation.

$2 w^{2} + 9 w - 10 - 6 w = 0$

Step 1.2

Subtract $6 w$ from $9 w$ .

$2 w^{2} + 3 w - 10 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 2$ , $b = 3$ , and $c = - 10$ into the quadratic formula and solve for $w$ .

$\frac{- 3 \pm \sqrt{3^{2} - 4 \cdot (2 \cdot - 10)}}{2 \cdot 2}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $3$ to the power of $2$ .

$w = \frac{- 3 \pm \sqrt{9 - 4 \cdot 2 \cdot - 10}}{2 \cdot 2}$

Step 4.1.2

Multiply $- 4 \cdot 2 \cdot - 10$ .

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Step 4.1.2.1

Multiply $- 4$ by $2$ .

$w = \frac{- 3 \pm \sqrt{9 - 8 \cdot - 10}}{2 \cdot 2}$

Step 4.1.2.2

Multiply $- 8$ by $- 10$ .

$w = \frac{- 3 \pm \sqrt{9 + 80}}{2 \cdot 2}$

Step 4.1.3

Add $9$ and $80$ .

$w = \frac{- 3 \pm \sqrt{89}}{2 \cdot 2}$

Step 4.2

Multiply $2$ by $2$ .

$w = \frac{- 3 \pm \sqrt{89}}{4}$

Step 5

The final answer is the combination of both solutions.

$w = - \frac{3 - \sqrt{89}}{4}, - \frac{3 + \sqrt{89}}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$w = - \frac{3 - \sqrt{89}}{4}, - \frac{3 + \sqrt{89}}{4}$

Decimal Form:

$w = 1.60849528 \dots, - 3.10849528 \dots$